Elliptic curve isogeny class with Cremona label 19950k (LMFDB label 19950.m)

• Label: 19950k
• Number of curves: $4$
• Conductor: $19950$
• CM: no
• Rank: $1$

Elliptic curves in class 19950k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19950.m4	19950k1	\([1, 1, 0, 75, -1875]\)	\(2924207/102144\)	\(-1596000000\)	\([2]\)	\(8192\)	\(0.44583\)	\(\Gamma_0(N)\)-optimal
19950.m3	19950k2	\([1, 1, 0, -1925, -31875]\)	\(50529889873/2547216\)	\(39800250000\)	\([2, 2]\)	\(16384\)	\(0.79241\)
19950.m1	19950k3	\([1, 1, 0, -30425, -2055375]\)	\(199350693197713/547428\)	\(8553562500\)	\([2]\)	\(32768\)	\(1.1390\)
19950.m2	19950k4	\([1, 1, 0, -5425, 111625]\)	\(1130389181713/295568028\)	\(4618250437500\)	\([2]\)	\(32768\)	\(1.1390\)

Rank

The elliptic curves in class 19950k have rank \(1\).

Complex multiplication

The elliptic curves in class 19950k do not have complex multiplication.

Modular form 19950.2.a.k

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.